Interpretable models for forecasting high-dimensional functional time series

2026-03-30

AI Summary

This study addresses the challenge of modeling high-dimensional functional time series characterized by both temporal dependence and cross-sectional correlation, where conventional approaches often lack interpretability. The authors propose a decomposition framework that integrates functional analysis of variance (FANOVA) with a functional factor model, explicitly separating the observed data into interpretable deterministic components—such as regional or gender effects—and a stochastic residual process. Building upon this decomposition, the method enables joint forecasting that balances model interpretability with predictive accuracy. Empirical validation on Japanese age-specific mortality rates across prefectures from 1975 to 2023 demonstrates substantial improvements in both point and interval forecast performance. Furthermore, the approach elucidates key demographic drivers, offering policymakers a transparent and reliable basis for decision-making.

Abstract

We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. We implement a functional analysis of variance (FANOVA) to decompose high-dimensional functional time series, such as subnational age- and sex-specific mortality observed over years, into two distinct components: a deterministic mean structure and a residual process varying over time. Unlike purely statistical dimensionality-reduction techniques, the FANOVA decomposition provides a direct and interpretable framework by partitioning the series into effects attributable to data-specific factors, such as regional and sex-level variations, and a grand functional mean. From the residual process, we implement a functional factor model to capture the remaining stochastic trends. By combining the forecasts of the residual component with the estimated deterministic structure, we obtain the forecasted curves for high-dimensional functional time series. Illustrated by the age-specific Japanese subnational mortality rates from 1975 to 2023, we evaluate and compare the accuracy of the point and interval forecasts across various forecast horizons. The results demonstrate that leveraging these interpretable components not only clarifies the underlying drivers of the data but also improves forecast accuracy, providing more transparent insights for evidence-based policy decisions.

Problem

• high-dimensional functional time series
• forecasting
• interpretability
• FANOVA
• mortality forecasting

Innovation

• functional ANOVA
• high-dimensional functional time series
• interpretable forecasting
• functional factor model
• mortality forecasting